The Zero-Beat Method of Frequency Discrimination*C. F. SHEAFFERt, ASSOCIATE, I.R.E.

Summary-A method of frequency discrimination in which thefrequency of balance is determined solely by the frequency of the con-trolling oscillator is explained. The method utilizes the phase turn-over, which occurs at zero beat, between two beat sources when one ofthe beating signals is dephased by 90 degrees before it is applied to oneof the beat detectors. A network is inserted in one of the beat sourceswhich shifts its phase an additional .90 degrees and makes its outputa direction function of the frequency. The beats are then amplifiedand supplied to a balanced rectifier, from which a direct voltage isavailable which changes polarity with the direction of frequency devia-tion.

S INCE the advent of the practical frequency-modulation system of radio transmission, therehas been a constant search for a method of fre-

quency stabilization which would be both simple andeffective.

Each system in present use has its particular ad-vantages and weak points. It seems that the mosteffective systems either require a multitude of fre-quency-doubler stages, or a multitude of frequency-divider stages, which renders either of these systemsrather cumbersome for use in portable equipment.The Crosby circuit,1 which makes use of a reactance-

tube-controlled oscillator, stabilized by a discrimina-tor, approaches the ideal but has several fundamentalweaknesses. Perhaps the predominating one is the factthat, in this method, the discriminator must be aphase-shifting device whose elements are subject totemperature, mechanical, and other variations whichrequire the use of temperature control and precau-tionary design considerations in order to secure ade-quate stability.

If a system of discrimination could be devised whichwould not depend upon tuned circuits, this weak pointcould be hurdled. If, further, the discriminator outputcould be made as high as desired without affecting thefrequency of balance, the problem of securing adequatestabilization would not be difficult. Such a system2 hasbeen devised and is the subject of this paper.The various elements involved in the device, and

their arrangement, are indicated in Fig. 1. The fre-quency modulation, as well as the automatic fre-quency control, is accomplished by utilizing the con-trol of the so-called reactance tube over the frequencyof a tuned-circuit oscillator. In the arrangement ofFig. 1, the oscillator operates at a frequency of 2650kilocycles, and is followed by a buffer amplifier whichdrives a frequency-doubler stage. The discriminatorvoltage stability is acquired by utilizing a highlystable crystal-controlled oscillator adjusted to give anoutput frequency of 5300 kilocycles. In detector 1, the

*Decimal classification: R355.6X R414. Original manuscriptreceived by the Institute, November 13, 1941.

t U. S. Signal Corps, Oklahoma City, Oklahoma.1 M. G. Crosby, "Reactance tube frequency modulators," RCA

Rev., vol. 5, pp. 89-96; July, 1940.2 U. S. Patent No. 2,274,434, February 24, 1942.

output of the frequency doubler is mixed with that ofthe crystal oscillator and the resulting beat is selectedin the plate circuit. The phase of the crystal output isshifted by 90 degrees and mixed with the doubler out-put in detector 2 to provide a second source of beatfrequency. We must now consider the relationshipbetween these sources of beat frequency. If the fre-quency of the doubler output is equal to that of thecrystal oscillator, the beats will have zero frequency.If the doubler frequency is not equal to the crystal fre-

CRYSTAL _ _ JOSCILLATOR5300 KC. -iIi£

--.-.1~~--

Fig. 1-Schematic diagram of the zero-beat frequency-discriminatorsystem utilized as a control element in a frequency-modulationtransmitter.

quency, beats occur as a result of the falling in andout of step of the two radio-frequency voltages. Sincethe phase of the crystal-frequency supply fed to de-tector 2 lags that fed to detector 1 by 90 degrees, thetwo beats will have a phase separation of 90 degreeswhich is independent of the beat frequency. If thephase of the doubler output is advancing with respectto that of the crystal, that is, if its frequency is higher,the voltages applied to detector 2 fall in step onequarter of a beat cycle later than those applied to de-tector 1. In this case, therefore, the beat outputs ofthe detectors will have the relationship Edl=jEd2. If,however, the phase of the doubler frequency is retard-ing with respect to that of the crystal, the radio fre-quencies applied to detector 2 will fall out of step onequarter of a beat cycle after the voltages at detector 1were in step. The phase relationship between the de-tector outputs in this case will be Edl =-jEd2. Wethus see that a relative phase reversal between the beatsupplies takes place as the frequency difference goesthrough zero, that is, at zero beat.

It now becomes apparent that if one of the beatsupplies can be given an additional 90-degree shiftwhich will hold for all beat frequencies of importance,

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and its output can be made a linear function of thefrequency, we will have at hand the elements of a fre-quency discriminator. For all practical purposes thisis accomplished by the network in the plate circuitof detector 2. The beat voltage at the output of de-tector 1 and that at the output of the shifter device,therefore, will be either in phase or out of phase, de-pendent upon whether the doubler frequency has de-viated in a positive or negative direction. There re-mains, therefore, only the problem of amplifying andsupplying the two derived beats to the balanced recti-fier in a manner that will make available a rectifieddifference voltage proportional to the deviation anddirection of deviation of the doubler frequency. Thisis accomplished by the two amplifiers and their as-sociated output transformers which are connected soas to provide voltages at the plates of the two diodeswhich represent, respectively, the sum and differenceof the two beat voltages.

Fig. 2-An equivalent circuit of the 90-degree beat shifter.

Since the output of amplifier 2 is directly propor-tional to the beat frequency, the equations for thevoltages applied to the diodes of the balanced rectifiermay be written as

El = Eal + KfdEd2/2E2= Eal -KfdEd2/2.

We shall call the resulting rectified voltages Er1 andEr2. The output of the duodiode rectifier from cathodeto cathode will be

Er - Er2 = (Eal + KfdEd2/2) - (Eal- KfdEd2/2)= KfdEd2.

In these equations the frequency deviationfd is eithera positive or negative quantity, dependent upon thedirection of deviation.The output, when filtered, is therefore a positive or

negative direct voltage whose amplitude and polarityare dependent upon the deviation and direction ofdeviation of the doubler frequency from that of thecrystal oscillator. The voltage is zero only at zerobeat and any deviation from the zero-beat value auto-matically produces a frequency-correcting voltage,for application to the reactance-tube grid, which actsto limit the deviation of the oscillator frequency.

This discriminator has two very important advan-tages over the tuned-circuit type. The first, of course,is that its balance frequency is fixed by the crystal,and therefore does not in any way depend upon un-stable, temperature-sensitive, tuned circuits for sta-

bility. The correct adjustment for the oscillator tuningis always the setting which gives zero discriminator-rectifier output, and therefore a means is continuouslyavailable for readjusting the oscillator frequency dur-ing operation, which makes possible a maximum ofaccuracy at all times. A meter may be provided forthis purpose and can be calibrated to indicate the fre-quency deviation covering the tolerance range.The second advantage is that the two beat sources

may be amplified to any desired extent without affect-ing the frequency of balance, and therefore the sensi-tivity of the device is limited only by practical circuitcomponents.

It is required that the two amplifiers be flat through-out the modulation band of the frequency-modulatedsignal, and that their phase characteristics be identical.The output transformers must, therefore, be high-qual-ity devices with electrostatic shielding between the pri-mary and secondary windings. Discrimination atrelatively low deviation level is indicated if trans-formers are used as coupling devices, but this imposesno serious restriction on the amount of control whichcan be attained.A further requirement is that the 90-degree network

in the plate of detector 2 shift the phase by 90 degreesfor all frequencies important to the system. The meanswhereby this is accomplished is therefore an importantpart of the device. An equivalent circuit of the net-work is shown in Fig. 2. The output/input voltageratio may be written as

Er (R + jwL)E, (R + Rp) + j(coL -1/GC)

Rationalizing this expression we obtain

Er R(R + Rp) + cwL(wL - 1/coC)E8 (R + Rp)2 + (coL - 1/coC)2

(R + R,)coL - R(coL - 1/coC)

(R + Rp)2 + (coL - 1/COC)2

(1)

(2)

If the numerator of the first term of (2) can beequated to zero for all frequencies, the network willthen shift the phase of any frequency passed throughit by exactly 90 degrees. This, of course, is impossible.Ho-.-,-ever, suppose that, within the frequency band ofimpci tance, values are selected so that 1/cC>»oL.The numerator could then be written as approximatelyR(R+Rp) -L/C, which contains no frequency termand therefore may be equated to zero.

It is also required that the voltage ratio be a linearfunction. This is realized if the second term of equation(2) is a direct function of the frequency. Suppose thatin addition to the above (R+R)2«<<(1/1C)2. Equa-tion (2) then reduces to E,I/E8=jwCR.

Design procedure is, therefore, based upon theselection of circuit components which meet, to a suf-ficient extent, the above conditions.An experimental unit based on Fig. 1 was built up

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in the workshop and experiment indicated that thediscriminator operation was entirely satisfactory. Asensitivity of the order of 20 volts per kilocycle waspossible throughout a band of plus or minus 15 kilo-cycles, even though small tubes and limited supplyvoltage was used. Symmetry of output with respect topositive and negative frequency deviation is a char-acteristic of this discriminator, as is also linearity.

The device is completely electronic in principle andcan be made sufficiently compact for use in portableand semiportable transmitters. It forms the basis fora control system which can quite capably maintain thestability well within the requirements of the FederalCommunications Commission for frequency-modula-tion broadcast transmitters.

Cosmic Static*GROTE REBERt, ASSOCIATE, I.R.E.

Summary-Cosmic static is defined as electromagnetic radiationwhich may be detected by radio receiving equipment and which hasextraterrestrial origin. A highly directive system for detecting and re-cording these radiations is described and analyzed.

Data are given on the variations in intensity of cosmic static in rela-tion to various regions of the galaxy. The effects of interference arediscussed.

It is suggested that cosmic static is the eguivalent of thermal agita-tion in which all space is the conductor and the input terminals of thedetecting equipment are projected by means of an antenna system tosame far-distant part of space.

INTRODUCTION', OSMIC STATIC" is used throughoutthis papertv to designate those electromagnetic radiations,

the sources of which are not associated with theearth or its atmosphere, and which have wavelengthssuch that they are detectable by ordinary radio re-ceiving equipment. Some time ago the initial results'and a short description of the apparatus2 used in thiswork were published. Since then the performance ofthis equipment has been closely scrutinized to under-stand better what the requirements for the measure-ment of this phenomenon are and how to meet them.Since both cosmic static and thermal-agitation noisegenerated in the receiver are continuous spectra ofconstant amplitude over the limited frequency rangewithin the acceptance band of the receiver, there isonly a single parameter to distinguish one from theother, namely magnitude. These two disturbances arecontinuous spectra from separate sources and will addtogether on a power basis. Fortunately the absolutemagnitude of thermal-noise energy has been well es-tablished and may be used as a reference level forestimating the magnitude of cosmic static.

COLLECTOR SYSTEMThe major piece of apparatus used in this work is

shown in Figs. 1, 2, and 3. The electromagnetic energyfrom space is collected by a mirror and captured by a

* Decimal classification: R114. Original manuscript receivedby the Institute, August 27, 1941: revised manuscript received,May 8, 1942.

t 212 W. Seminary Ave., Wheaton, Illinois.l G. Reber, "Cosmic static," Astrophys. Jour., vol. 91, p. 621;

June, 1940.2 G. Reber, "Cosmic static," PROC. I.R.E., vol. 28, pp. 68-71-

February, 1940.

drum which acts as a black body. No direct measure-ment has been made of the angular resolving power ofthis combination. At 160 megacycles, the mirror has an

Fig. 1-Collector pointed to declination +40 degrees. Small drumat focal point for operation at 900 megacycles. Mirror diameter,31.4 feet, focal length, 20 feet.

aperture of 5.1 wavelengths and a focal length of 3.25wavelengths. Experiments with models and theoreticalinvestigation indicate the half-amplitude points onpolar curves of power sensitivity are about 6 degreesapart in the plane of the magnetic vector and 8 degreesapart in the plane of the electric vector. These valuesare somewhat larger than estimated in a previouspaper. Fig. 4 shows the antenna wire inside of the drumand the transmission line going to the receiver. This

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